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This work derives the linearized equations of motion, the Lagrangian density,the Hamiltonian density, and the canonical angular momentum density for generalperturbations [$\propto \exp(im\phi)$ with $m=0,\pm 1,..$] of a geometricallythin self-gravitating, homentropic fluid disk including the pressure. Thetheory is applied to ``eccentric,'' $m=\pm 1$ perturbations of a geometricallythin Keplerian disk. We find $m=1$ modes at low frequencies relative to theKeplerian frequency. Further, it shown that these modes can have negativeenergy and negative angular momentum. The radial propagation of these lowfrequency $m=1$ modes can transport angular momentum away from the inner regionof a disk and thus increase the rate of mass accretion. Depending on the radialboundary conditions there can be discrete low-frequency, negative-energy, $m=1$modes.Comment: 24 pages, 8 figure

Negative Energy And Angular Momentum Modes Of Thin Accretion Disks